Hi, my name is Nawe and this is my Ezreal guide, I've been playing Ezreal as my main adc for a while now and I tought I'd give my build and knowledges to everyone :).
(This is not going to be a long guide explaining all his skills etc, telling you a quite good build.

The normal Carry runes, The MR on blue is good from taking harass from agressive supports like:
Taric and Sona.
The Armor on yellow is just good against Adc's who REALLY has a hard time getting through that layer of armor.
For example: Caitlyn, Miss fortune and Sivir.

The normal adc masteries:
21 in Offence, 9 in defence, nothing really much there (See top of the guide)

Flash is a MUST for ANY gap closer teams !
Cleanse is a good spell to avoid all the kind of CC the enemy team has, if the enemy has a Leona, Cleanse is highly advised.

Start off with boots 3 pots, Ezreal low base movement speed makes this extremely usefull, especially against champions who skillshots.
The rush for the Vampiric spectre gives you Decent sustain in lane (Altough if you have a Soraka or Sona, DO NOT RUSH THIS ITEM), Rush something else (A bf sword) Greaves or a Phage)
Get either Phage or Sheen first, let me explain why:
Phage gives you nice damage, health and ability to kite, and the Sheen procs with your Q so if you want to poke alot, it's a great item to get early.
After your bloodthirster and Greaves buy your Trinity force, after that if you feel like the other team starts stacking armor and you really need it, then buy it.
Otherwise after the Trinity force buy a ''Phantom Dancer'' This will give you great Movement speed with your Trinity force, and will really help you from your really slow movement speed.
So now your build contains 4 items: Berserker's greaves, Bloodthirster, Trinity force and Phantom dancer. Now get some survivability, Guardian's angel if you're getting focused alot (And you and your team is not getting completely demolished), Warmogs if they got a fed bruiser or alot of bruisers.
And the last thing you should get should be the Infinity edge ! For the awesome late game damage !

Always stay at the back of your team and when the entire enemy team is lined up, ult them and just do free damage on them.

Pros:
Fun to play
Good escape/engage
Great overall damage mid-late game
Lots of poke
He's together with Sona

Cons
Skillshot based
Low base movement speed
quite bad late game (If you're not doing good)
Hard to master
Easy to shutdown
He's not together with Taric